Question

if 4^{x}-4^{x-1}=24 ,find (2x)^{x}....​

Answer 1

Answer: 25√5

$=>4^{x}-4^{x-1}=24 \\ =>4^x-4^{x}×4^{-1}=24 \\=> 4^{x}-4^{x}/4=24 \\=> 4^{x}(1-1/4)=24 \\ =>4^{x}(4-1/4)=24 \\=> 4^{x}=24×3/4 \\ =>4^{x}=32 \\ =>4^{x}=32 \\ =</p><p>2^{2x}=2^{5} (base\:are\:equal)\\ compare\:the\:exponent \\ 2x=5 \\ x=5/2 \\ putting\:the \:value\:of\:X \\ (2x)^{x}=(2×5/2)^{5/2} \\ =>5^{5/2} \\ =>5^(5×1/2) \\ =>\sqrt5^{5} \\ =>\sqrt5×5×5×5×5 \\=> 5×5\sqrt5 \\ =>25\sqrt5$